Question

In the given figure, rays OA, OB, OC, OD and OE have the common end point O. Show that ∠AOB + ∠BOC + ∠COD + ∠DOE + ∠EOA = 360°.

Answer 1

Let us draw a straight line.

,and form a linear pair. Thus, their sum should be equal to.

Or, we can say that:

(I)

Similarly,,and form a linear pair. Thus, their sum should be equal to.

Or, we can say that:

(II)

On adding (I) and (II), we get:

Hence proved.